无穷区间上分数阶微分方程的迭代解
Iterative Solutions of Fractional Differential Equations on Infinite Interval
DOI: 10.12677/AAM.2022.113154, PDF, HTML,    科研立项经费支持
作者: 胡晓蝶, 王 颖*, 闽梦琪, 谷德阳：临沂大学，数学与统计学院，山东 临沂
关键词: 分数阶微分方程；迭代解；无穷区间；Fractional Differential Equation； Iterative Solution； Infinite Interval
摘要: 本文主要研究无穷区间上的分数阶微分方程，应用单调迭代方法, 在一定的条件下，得到了方程的极值解和解的迭代序列。
Abstract: In this paper, we mainly investigate the fractional differential equation on infinite interval. Under certain conditions, we establish the existence of extremal solutions as well as iterative schemes by employing the monotone iterative technique.
文章引用：胡晓蝶, 王颖, 闽梦琪, 谷德阳. 无穷区间上分数阶微分方程的迭代解[J]. 应用数学进展, 2022, 11(3): 1412-1419. https://doi.org/10.12677/AAM.2022.113154

参考文献

[1] Kueser, A. (1996) Untersuchung und asymptotische darstellung der intergrale genwisser differ- ential gleichungen bei grossen werthen des arguments. Journal fu¨r die Reine und Angewandte Mathematik, 116, 178-212.
[2] Agarwal, P.R. and O’Regan, D. (2001) Infinite Interval Problems for Differential, Difference and Integral Equations. Kluwer Academic Publishers, Dordrecht. [Google Scholar] [CrossRef] 
[3] Zhao, X. and Ge, W. (2010) Unbounded Solutions for a Fractional Differential Boundary Value Problems on the Infinite Interval. Acta Applicandae Mathematicae, 109, 495-505. [Google Scholar] [CrossRef] 
[4] Liang, S. and Zhang, J. (2011) Existence of Three Positive Solutions of m-Point Boundary Value Problems for Some Nonlinear Fractional Differential Equations on an Infinite Interval. Computers and Mathematics with Applications, 61, 3343-3354. [Google Scholar] [CrossRef] 
[5] Liang, S. and Zhang, J. (2011) Existence of Multiple Positive Solutions for m-Point Fractional Boundary Value Problems on an Infinite Interval. Mathematical and Computer Modelling, 54, 1334-1346. [Google Scholar] [CrossRef] 
[6] Zhang, X. and Zhong, Q. (2018) Triple Positive Solutions for Nonlocal Fractional Differential Equations with Singularities Both on Time and Space Variables. Applied Mathematics Letters, 80, 12-19. [Google Scholar] [CrossRef] 
[7] Wang, F., Liu, L. and Wu, Y. (2019) Iterative Unique Positive Solutions for a New Class of Nonlinear Singular Higher Order Fractional Differential Equations with Mixed-Type Boundary Value Conditions. Journal of Inequalities and Applications, 2019, Article No. 210. [Google Scholar] [CrossRef] 
[8] Tan, J., Zhang, X., Liu, L. and Wu, Y. (2021) An Iterative Algorithm for Solving n-Order Fractional Differential Equation with Mixed Integral and Multipoint Boundary Conditions. Complexity, 2021, Article ID: 8898859. [Google Scholar] [CrossRef] 
[9] Podlubny, I. (1999) Fractional Differential Equations, Vol. 198. Academic Press, San Diego, CA.
[10] Miller, K.S. and Ross, B. (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York.
[11] Liu, Y. (2002) Boundary Value Problem for Second Order Differential Equations on Unbounded Domain. Acta Analysis Functionalis Applicata, 4, 211-216.
[12] Corduneanu, C. (1973) Integral Equations and Stability of Feedback Systems. Academic Press, New York.

为你推荐